The maps for each border crossing may vary from one version to another. You didn't make it apparent whether you are using MTW 'out of the box' (v1.0), MTW patched (to v1.1) or with Viking Invasion expansion ("V.I." aka v2.01).

For comparison purposes, I'm referring to VI (v2.01).

If you click on Kiev to highlight it and look at the info parchment, you should see :-

"Armies meeting here can expect to fight on the following terrain" and a description (my emphasis). This will only apply to battles as a result of local rebellions or faction re-emergences which pop up within this province.

Leaving Kiev highlighted and the parchment open, hover your cursor over each neighbouring province and you'll see the map type applicable if you attack out of Kiev.

Now click on, to highlight, Crimea, for example. Open the province parchment again and hover your cursor over Kiev. Last time I looked, that said river. Try other neighbouring provinces in a similar way. I think Khazar->Kiev is also river and that's generally where the Horde will be attacking Kiev from.

Kiev->Khazar is not a river and there seem to be several examples of this, where the terrain applicable to a border crossing differs according to which direction the attack is going. Strange but true.

HTH